STATS-003: Sampling
In section STATS-001, we learned that a sample is a portion (smaller set) of a population used in order to study a larger population. In this section, we are going to discuss a bit more about samples, including some methods used for sampling a population. When gathering a sample, it is important that the sample has the same characteristics as the population that it is representing. (If the sample had different characteristics compared to the larger population, then that sample would not accurately represent the population.) When gathering a sample of a population, most statisticians use random sampling, which means that each member of a population has an equal chance of getting selected to be in the sample. There are four methods of random sampling: simple random sample, stratified sample, cluster sample and systematic sample. A simple random sample means that each sample of size " n " people has an equal chance of being selected for the sample. In other words, one group of n people will have the same chance of being selected for a sample as a different group of n people. This is the most common method of random sampling, and you may have done this in the past - pulling names out of a hat to select people is simple random sampling. A stratified sample takes the entire population and divides it into smaller groups (which are called "strata" (sing., "stratum")). You then take a proportionate (equal) number of people from each stratum, and those people are used for the sample. A cluster sample takes the entire population and divides it into clusters (smaller groups), and then you choose a certain number of clusters to be part of the sample. This is different from a stratified sample because in a stratified sample, you divide the population into groups and then pick n people from each group, whereas with a cluster sample, you divide the population into groups and then pick n entire groups. A systematic sample lists every member of the population in a list. You then randomly pick a starting point and then from there, take every n th item from the list. These n th items then become the sample. For example, if you have a list of 100 names and you wanted to use systematic sampling, you would pick a random starting point on that list and then pick every fifth (for example) person until you reached the end of the list. Each person that you picked will become part of the sample. There is also one method of sampling that is not random, and that is a convenience sample. A convenience sample simply involves using results that are easily available and/or accessible. An example of a convenience sample would be if you were asked to collect data on a population's favorite movie, and you simply called each of your friends and asked them to name their favorite movie. This would not be a random sample since your friends' phone numbers are easily available to you (since they are stored in your phone), and not every member of the overall population had an equal chance of being selected for the sample. One little extra note - if you have a graphing calculator, you can actually use it to generate a list of random numbers. Here's how: First, turn the calculator ON and then press the MATH key located here: This will open the math menu, which looks like this: In the math menu, use the arrow keys to scroll over to the "PRB" ("Probability") menu: Within the probability (PRB) menu, use the arrow keys again to scroll down to option 5: \text{randInt(} Press the ENTER key once you've highlighted this option, and \text{randInt(} should appear on-screen like this: There are three numbers that we must put into \text{randInt(} . The first number that we type in will be the smallest number that can appear in the list of randomly generated numbers. You can input any integer, but for this example, I will input the number 0 : After inputting the first number, we must press the comma key located here: After the comma, we must type the second number into the calculator. This second number we type will be the largest number that can appear in the list of randomly generated numbers. For this example, I will input the number 50 : After inputting the second number, we must press the comma key again: After this comma, we must type the third and final number into \text{randInt(} . This third number we type will be the amount of random numbers that the calculator will generate. (In this case, the amount of random numbers the calculator will generate between 0 and 50 .) For this example, I will input the number 5 (which means that the calculator will generate five random numbers between 0 and 50 ): After inputting this third number, press the ENTER key. The calculator will then display a list of random numbers like this: